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Math Help - Real problem with this coursework

  1. #1
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    Real problem with this coursework

    could i have help on parts B and C of this assignment please. Its really urgent :s




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  2. #2
    Grand Panjandrum
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    f(t) = 5 e^(-0.8 t) sin(2 pi t / 3)

    (b) find f'(t).

    Use the product rule:

    f'(t) = 5 d/dt[e^(-0.8 t)] sin(2 pi t /3) + 5 e^(-0.8 t) d/dt[sin(2 pi t / 3)]

    ......= 5 (-0.8) e^(-0.8) sin(2 pi t /3) + 5 e^(-0.8 t) (2 pi / 3) cos(2 pi t / 3)

    ......= 5 e^(-0.8 t) {(-0.8) sin(2 pi t /3) + (2 pi / 3) cos(2 pi t / 3)}

    (c) Solve f'(x) = 0 to determine the maximum deflection and when it occurs.

    f'(t) = 0 after cancelling the leading intrinscily non zero term gives:

    (-0.8) sin(2 pi t /3) + (2 pi / 3) cos(2 pi t / 3) = 0

    or:

    tan( 2 pi t / 3) = 2 pi / 2.4,

    so:

    2 pi t / 3 =arctan(2 pi / 2.4) ~= 1.206 + pi n, n=0, 1, 2, ...

    (only positive n will be considered as usually t is measured from the time
    of the disturbance to the system, so times <0 are meaningless) so:

    t = 0.573 + 3/2 n, n=0, 1, 2, ..

    Now as e^(-0.8 t) is a strictly decreasing function the deflection of
    maximum amplitude is the first of these, so it occurs at t=0.573, and is of
    amplitude:

    5 e^(-0.8*0.573) sin(2 pi*0.573 / 3) = 2.95

    RonL
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